A far-reaching and influential view in evolutionary biology claims that species are cohesive units held together by gene flow. Biologists have recognized empirical problems facing this view; after sharpening the expression of the view, we present novel conceptual problems for it. At the heart of these problems is a distinction between two importantly different concepts of cohesion, what we call integrative and response cohesion. Acknowledging the distinction problematizes both the explanandum of species cohesion and the explanans of gene flow that are central to the view we discuss. We conclude by tracing four broader implications for the study and conceptualization of species.